Parametric 3D geological modeling facilitates the efficient updating of geological models. A comprehensive review of existing geological modeling methods reveals that two critical issues need to be addressed for realizing parametric 3D geological modeling: (1) complex surface topology caused by direct interpolation of geological data creates a significant obstacle to the parametric characterization of irregular geometry of geological interfaces, and (2) expert knowledge input essential during modeling the complex geological bodies have not been formalized quantitatively and objectively, which poses another barrier to the automation of parametric geological modeling. In response, this work presents a parametric 3D geological modeling method achieving the parametric expressions of geological interfaces and automatic modeling for different geological bodies without manual interaction. In this study, the NURBS Surface Dynamic Topology (NURBS-SDT) method is proposed to regularize the complex topological structure of the geological interfaces, thereby expressing them parametrically. Furthermore, 3D coordinates are converted into the control parameters of the geological interface geometry. On the other hand, subjective expert knowledge input is translated into objective modeling rules through the proposed Boolean Logic Sequence of Oriented Geological Interfaces (BLSOGI) method, which means different geological bodies can be automatically modeled. A practical application to a city in southern China demonstrates a 570-fold increase in efficiency of model updating by the proposed method compared to the conventional interactive approach. The comparison with four other representative automatic and semi-automatic methods also shows the higher applicability of the proposed method in modeling complex strata. Thus, this study can greatly improve the efficiency of the engineering geological investigation and design.